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Q.

Equal volumes of water and alcohol when put in similar calorimeters take 100 sec and 74 sec respectively to cool from 500C to 400C. The thermal capacity of each calorimeter is numberically equal to the volume of either liquid. The specific gravity of alcohol is 0.8. If the specific heat capacity of water is 1 cal/gm, the specific heat capacity of alcohol will be

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a

0.6 cal/gm-0C

b

0.8 cal/gm-0C

c

1.6 cal/gm-0C

d

1.8 cal/gm-0C

answer is A.

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Detailed Solution

Let V be the volume of either liquidThermal capacity of each calorimeter is V cap per  0CMass of water = V × 1 = V gMass of alcohol = V × 0.8 = 0.8 VgRate of colling of water,  = 1100[V(50-40)+V×1×(50-40)] = V5 cal/secRate of cooling of alcohol   = 174[V(50-40)+S×0.8V×10]  = 174[10V + 8V×S ] Now    174[10V + 8V×S] = V5∴ s = 0.6 cal/g0C
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Equal volumes of water and alcohol when put in similar calorimeters take 100 sec and 74 sec respectively to cool from 500C to 400C. The thermal capacity of each calorimeter is numberically equal to the volume of either liquid. The specific gravity of alcohol is 0.8. If the specific heat capacity of water is 1 cal/gm, the specific heat capacity of alcohol will be